Type the following into the Input field
1) a=1
2) f(x) = a x^2 {a short cut for x^2 you can hold the <alt key> while pressing the 2}
You now see the parabola f(x) = x^2
Click on a=1 in Algebra window and to “Show Object”
Use the Move Tool to change ‘a’
Right click on a=1 in Algebra window and select “Properties”
Click on the “Slider” tab and change the increment to 1
Click on the Function f, select “Show Trace” and close
Move the slider left and right.

The vertex form of the parabola is: f(x) = a (x - h)2 + k.
What would you need to add to this worksheet to use this form?
Add these items and retype f(x).
Show the new sliders. Move the sliders left and right to observe the results.

The general form of the parabola is: g(x) = a x2 + b x + c.
What would you need to add g(x) to the worksheet to use this form?
Add these items and type g(x).

Show the new sliders. Move the sliders left and right to observe the results.
Can you manipulate the f(x) curve to overlap that of the g(x)?
Which sliders would you move left and right?

## Creating a Parabola

Type the following into the Input field1) a=1

2) f(x) = a x^2 {a short cut for x^2 you can hold the <alt key> while pressing the 2}

You now see the parabola f(x) = x^2

Click on a=1 in Algebra window and to “Show Object”

Use the Move Tool to change ‘a’

Right click on a=1 in Algebra window and select “Properties”

Click on the “Slider” tab and change the increment to 1

Click on the Function f, select “Show Trace” and close

Move the slider left and right.

The vertex form of the parabola is: f(x) = a (x - h)2 + k.

What would you need to add to this worksheet to use this form?

Add these items and retype f(x).

Show the new sliders. Move the sliders left and right to observe the results.

The general form of the parabola is: g(x) = a x2 + b x + c.

What would you need to add g(x) to the worksheet to use this form?

Add these items and type g(x).

Show the new sliders. Move the sliders left and right to observe the results.

Can you manipulate the f(x) curve to overlap that of the g(x)?

Which sliders would you move left and right?

A B Cron, Created with GeoGebra